FprEN ISO 23691

SLOVENSKI STANDARD
oSIST prEN ISO 23691:2024
01-november-2024
Mikrobiologija v prehranski verigi - Ugotavljanje in uporaba kardinalnih vrednosti
(ISO/DIS 23691:2024)
Microbiology of the food chain - Determination and use of cardinal values (ISO/DIS
23691:2024)
Mikrobiologie der Lebensmittelkette - Bestimmung und Verwendung von Kardinalwerten
(ISO/DIS 23691:2024)
Microbiologie de la chaîne alimentaire - Détermination et utilisation des valeurs
cardinales (ISO/DIS 23691:2024)
Ta slovenski standard je istoveten z: prEN ISO 23691
ICS:
07.100.30 Mikrobiologija živil Food microbiology
oSIST prEN ISO 23691:2024 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

oSIST prEN ISO 23691:2024
oSIST prEN ISO 23691:2024
DRAFT
International
Standard
ISO/DIS 23691
ISO/TC 34/SC 9
Microbiology of the food chain —
Secretariat: AFNOR
Determination and use of cardinal
Voting begins on:
values
2024-09-09
Microbiologie de la chaîne alimentaire — Détermination et
Voting terminates on:
utilisation des valeurs cardinales
2024-12-02
ICS: 07.100.30
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
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This document is circulated as received from the committee secretariat.
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Reference number
ISO/DIS 23691:2024(en)
oSIST prEN ISO 23691:2024
DRAFT
ISO/DIS 23691:2024(en)
International
Standard
ISO/DIS 23691
ISO/TC 34/SC 9
Microbiology of the food chain —
Secretariat: AFNOR
Determination and use of
Voting begins on:
cardinal values
Microbiologie de la chaîne alimentaire — Détermination et
Voting terminates on:
utilisation des valeurs cardinales
ICS: 07.100.30
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
AND MAY NOT BE REFERRED TO AS AN
INTERNATIONAL STANDARD UNTIL
PUBLISHED AS SUCH.
This document is circulated as received from the committee secretariat.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
© ISO 2024
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
STANDARDS MAY ON OCCASION HAVE TO
ISO/CEN PARALLEL PROCESSING
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TO SUBMIT, WITH THEIR COMMENTS,
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NOTIFICATION OF ANY RELEVANT PATENT
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Website: www.iso.org
Published in Switzerland Reference number
ISO/DIS 23691:2024(en)
ii
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Principle . 6
4.1 General .6
4.2 Mathematical models .6
4.3 Process of cardinal values and food correction factor determination .9
4.4 Determination of the maximum specific growth rate .9
4.4.1 Binary dilution OD-based method .10
4.4.2 Direct plating method .11
4.5 Cardinal parameters determination .11
4.6 Correction factor determination . 12
4.7 Validation . 13
4.8 Use of cardinal values and food correction factor in predictions .14
5 Diluents, culture media and reagents . 14
6 Laboratory equipment and apparatus. 14
7 Experimental design and data collection .15
7.1 General . 15
7.2 Preparation of culture and medium . 15
7.2.1 Choice and storage of studied strain . 15
7.2.2 Preparation and inoculation of the microbial culture .16
7.2.3 Preparation of the modified nutrient broth .16
7.3 Levels per factor to estimate cardinal parameters .17
7.3.1 General .17
7.3.2 Temperature .17
7.3.3 pH .18
7.3.4 Water activity.19
7.3.5 Inhibitory compounds . 20
7.4 Experimental design to estimate the maximum specific growth rate from the binary
dilution OD-based method .21
7.5 Experimental design to estimate the maximum specific growth rate from the direct
plating method . 22
7.6 Determination of the food correction factor based on a challenge test . 22
7.7 Validation . 23
8 Expression of the results: Estimation of the growth parameters .23
8.1 General . 23
8.2 Assessment of maximum specific growth rate at each level of intrinsic or extrinsic
factors (first step) .24
8.2.1 General .24
8.2.2 Assessment of maximum specific growth rates from direct plating data .24
8.2.3 Assessment of maximum specific growth rates by OD-based binary dilution
method .24

8.3 Assessment of cardinal values and optimum growth rate in broth, μμ (second
Broth
step) .
8.4 Assessment of C (third step) . 25
f
8.5 Validation (fourth step) . 26
9 Use of cardinal values to perform microbial growth predictions .26
9.1 General . 26

iii
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
9.2 Prerequisites for growth predictions .27
9.3 Using cardinal values to simulate growth . 28
9.3.1 Growth simulation at a static given temperature . 28
9.3.2 Growth prediction with dynamic time-temperature scenario . 29
9.3.3 Growth simulation at a static condition of temperature, pH and a . . 30
w
10 Test report .32
11 Quality assurance .32
Annex A (informative) Indicative list of tools for primary and secondary fittings and
simulations.33
Annex B (informative) Guidance to obtain different aw values when using different humectants
in broth .35
Annex C (informative) Growth rate determination .36
Annex D (informative) Plate design .40
Annex E (informative) Example of the use of cardinal values for growth simulation and its
variation . 41
Bibliography .44

iv
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO [had/had not] received notice of
(a) patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
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For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 34, Food products, Subcommittee SC 9,
Microbiology.
v
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
Introduction
Under the general principles of the Codex Alimentarius on food hygiene, it is the responsibility of the Food
Business Operators (FBO) to control microbiological hazards in foods and to manage microbial risks.
Therefore, the FBO shall implement validated control measures, within the hazard analysis and critical
control point (HACCP) system, and conduct studies in order to investigate compliance with the food safety
criteria throughout the food chain.
In the framework of Microbial Risk Assessment (MRA), several complementary approaches are developed
to estimate risks posed by pathogens or spoilage microorganisms in the food chain. MRA is adopted by
regulators under the auspices of the international agency for setting food standards. Predictive Microbiology
is one of the recognized scientific approaches used to validate control measures within the HACCP system,
as well as to assess microbiological safety and quality of food, food production processes, food storage
conditions, and food preparation recommendations dedicated to consumers.
Therefore, this document provides technical rules, procedures and calculations to estimate the cardinal
values of a microorganism of concern and use them in combination with challenge tests results to simulate
and predict its growth in the raw materials, intermediate or end-products under reasonably foreseeable
food processes, storage and use conditions.
To do so, different sections are developed:
— to identify the environmental factor(s) in scope (e.g. Temperature, pH, a , organic acids),
w
— to define the appropriate experimental design,
— to estimate the cardinal values of a microorganism in broth medium,
— to perform a challenge test in the matrix of interest and derive the food correction factor and the
maximum microbial population density,
— to use the cardinal values and the food correction factor to predict the growth of the studied
microorganism in different conditions of interest (e.g. changes in time and temperature throughout the
chill chain, changes in formulation with addition of organic acids or preservatives).
Regulatory authorities may have specific recommendations, and these differences have been included
as much as possible in this document. It is however possible that additional requirements need to be
incorporated to get a regulatory approval of the study.
The use of the ISO 23691 involves expertise in relevant fields such as food microbiology, predictive
microbiology and statistics. This expertise encompasses an understanding of sampling theory and design
of experiments, statistical analysis of microbiological data and overview of scientifically recognized and
available mathematical concepts used in predictive microbiology.

vi
oSIST prEN ISO 23691:2024
DRAFT International Standard ISO/DIS 23691:2024(en)
Microbiology of the food chain — Determination and use of
cardinal values
WARNING — In order to safeguard the health of laboratory personnel, it is essential that tests for
detecting target microorganism(s) are only undertaken in properly equipped laboratories, under
the control of a skilled microbiologist, and that great care is taken in the disposal of all incubated
materials. Persons using this document should be familiar with normal laboratory practice. This
document does not purport to address all of the safety aspects, if any, associated with its use. It is the
responsibility of the user to establish appropriate safety and health practices.
1 Scope
This document establishes basic principles and specifies requirements and methods to determine the
cardinal values of bacteria and yeast strains and use them to predict microbial growth.
Four main steps are required: (1) Determination of the cardinal values in culture medium, (2) Determination
of the correction factor in the target food, (3) Validation of the model and (4) Simulations.
Four environmental factors are considered: temperature, pH, a and inhibitors (e.g. organic acids).
w
NOTE Microbial competition is not considered as an inhibitor in this standard and can be addressed by proper
modelling approaches.
The determination of cardinal values requires a two-step approach:
— the determination of maximum specific growth rates of the studied strain grown in broth under a defined
range of values of the studied environmental factor(s), and
— the use of recognized predictive microbiology secondary models to fit the obtained experimental data to
obtain the cardinal values.
The use of cardinal values in microbial growth simulation is based on predictive microbiology primary and
secondary models. The cardinal values are combined with challenge test data to consider the matrix effect.
Depending on the goal of the growth simulation, it is important to account for variation of cardinal values
between strains within a bacterial or yeasts species.
Cardinal values are a good indicator of a strain growth ability for the studied environmental factors. They
are therefore used as criteria to select strains, in addition to their origin and virulence, when performing
growth challenge tests (standard ISO 20976-1) or in methods validation (ISO 16140 standards serie).
NOTE This document focuses on the determination of cardinal values for one strain. The same methodology can
be used to characterize multiple strains independently to cover biological strain variability and include these results
in the predictions.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 7218, Microbiology of food and animal feeding stuffs — General requirements and guidance for
microbiological examinations
ISO 11133, Microbiology of food, animal feed and water — Preparation, production, storage and performance
testing of culture media
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
ISO 20976-1:2019, Microbiology of the food chain — Requirements and guidelines for conducting challenge tests
of food and feed products — Part 1: Challenge tests to study growth potential, lag time and maximum growth rate
ISO 18787:2017, Foodstuffs — Determination of water activity
ISO 16140-2:2016, Microbiology of the food chain — Method validation — Part 2: Protocol for the validation of
alternative (proprietary) methods against a reference method
ISO 5127:2017, Information and documentation — Foundation and vocabulary
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
binary dilution
method used to stepwise dilute a microbial suspension with a constant dilution factor of 2 in each step
3.2
biological independent replicate
refers to an experiment that has been performed using a newly prepared culture and a newly prepared medium
3.3
cardinal factor
extrinsic (Temperature) and intrinsic characteristics (pH, a , inhibitors) for which cardinal values are derived
w
3.4
cardinal parameter
cardinal value
estimated minimum, optimum or maximum values of extrinsic and intrinsic factors (e.g. temperature, pH,
a , inhibitors) that characterize the growth of a given microbial strain
w
3.5
challenge test
study of the growth (or inactivation) of microorganism(s) artificially inoculated in food
3.6
coefficient of variation (CV)
ratio of the standard deviation to the mean
3.7
correction factor
dimensionless value used to link the broth and the food optimum growth rates. It is the ratio of the

optimum growth rate estimated in the studied matrix (μ ) to the optimum growth rate value estimated
Food

in broth (μ )
Broth
3.8
detection time (td)
time at which the optical density (OD) reaches the pre-defined target during the exponential growth
3.9
exponential growth phase
phase during which the multiplication of the microbial population is the fastest. It is in this phase that the
maximum specific growth rate is reached

oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
3.10
extrinsic factor
factor in the surrounding environment of the food or the broth, such as temperature or packaging gaseous
composition, which affects the growth kinetics of the microorganism
3.11
gamma concept
ɣ
the gamma concept establishes that intrinsic (e.g. pH, water activity, inhibitors) and extrinsic factors (e.g.
temperature, packaging gaseous composition) affect the maximum specific growth rate independently, using
linear and or non-linear functions e.g. ɣ(temperature), ɣ(pH), ɣ(water activity), ɣ(inhibitors), normalized
between zero (no growth) and one (optimum condition for growth). When combined, the effect of the factors
is multiplicative
3.12
gamma function
ɣ(X)
non linear, dimensionless function, normalized between zero (no growth) and one (optimum condition for
growth) describing the relative effect of a studied factor (X) on the maximum specific growth rate (e.g.
ɣ(temperature), ɣ(pH), ɣ(water activity), ɣ(inhibitors))
3.13
growth curve
graphic representation of the increasing number of living cells of a microbial population in any given
intrinsic and extrinsic condition over a period of time
3.14
inoculum
microbial suspension used to contaminate the studied food or broth at a desired concentration
3.15
intrinsic factor
factor related to the food matrix itself or the broth, such as nutrients, water activity, organic acids or pH, and
which affects the growth kinetics of the micro-organism
3.16
lag phase
phase, directly after inoculation, during which the microbial population is adapting to the environment,
before it enters the exponential growth phase (3.9)
3.17
lag time
λ
kinetic parameter in time unit to characterize the duration of the lag phase (3.16)
3.18
maximum specific growth rate
µ
max
-1
kinetic parameter (h ) to characterize the exponential growth phase (3.9), represented by the slope of the
curve showing the evolution of the natural logarithm of the population as a function of time, under constant
growth conditions When the maximum specific growth rate is estimated in food, this is noted µ
max.food
3.19
Minimal Inhibitory Concentration
MIC
estimated parameter representing the lowest concentration of an inhibitor that gives a value of maximum
specific growth rate of zero
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
3.20
modified broth
culture medium with specific composition (e.g. increased salt content) or characteristic (e.g. pH) to study
intrinsic factors
3.21
Monte Carlo simulation
iterative random sampling method that propagates variability about model parameters to approximate the
distribution of input variables. Monte Carlo simulations are extensively used in quantitative risk assessment
and decision making
3.22
optimum growth rate

μμ
highest value among the maximum specific growth rates, estimated at the optimum conditions for growth
of the microorganism in a studied food or broth
3.23
optimum growth rate in broth

μμ
Broth
highest value among the maximum specific growth rates in broth, estimated at the optimum conditions for
growth of the microorganism
3.24
optimum growth rate in food
μμ
Food
highest value among the maximum specific growth rates in the food, estimated at the optimum conditions
for growth of the microorganism

Note 1 to entry: μ is a statistical parameter and is not measured in the food.
Food

Note 2 to entry: μ is a mathematical result obtained when all studied factors are at their optimum values and the
Food
respective ɣ terms are equal to 1.
3.25
organizing laboratories
laboratories with responsibility for determining the cardinal values (3.4) and performing the simulations
Data collection and data analysis (including fitting and simulation) are performed in a single or in multiple
laboratories.
3.26
pH value
measure of the concentration of acidity or alkalinity of a material in an aqueous solution
[SOURCE: ISO 5127:2017, 3.12.2.29, modified — Notes 1 and 2 to entry have been removed.]
3.27
pKa
quantitative measure (negative base-10 logarithm) of the acid dissociation constant or Ka value, which
indicates the strength of an acid in solution (the lower the pKa value the stronger the acid)
3.28
primary model
mathematical model describing the changes of microbial concentration as a function of time under constant
and known conditions of intrinsic and / or extrinsic factor(s)
3.29
relative standard error
r
standard error (se) (3.31) divided by the parameter estimate and expressed as a percentage

oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
3.30
secondary model
mathematical model describing the effects of the intrinsic and / or extrinsic factor(s) (e.g. temperature, pH,
a ) on the parameters of the primary model (3.28) (e.g. maximum specific growth rate)
w
3.31
standard error
se
measure of the uncertainty associated with the estimated parameter or the overall model fit
3.32
stationary phase
phase in which the microbial population no longer increases (reaches and remains at its maximum
concentration)
3.33
strong acid
is characterized by its negative pKa. It ionizes completely in an aqueous solution by losing one proton.
Hydrochloric and sulfuric acids are examples of strong acids
3.34
uncertainty
refers to variation that originates from lack of or incomplete knowledge of some characteristics of a system.
It originates from parameter uncertainty and model uncertainty. Sources of parameter uncertainty include
lack of data, measurement errors, sampling errors and systematic errors. Sources of model uncertainty
include model structure, excluded variables, model resolution, extrapolation. The standard error represents
the uncertainty associated with the parameter
3.35
variability
refers to variation that is inherent to a given system, typically as a result of true heterogeneity of the studied
population and is irreducible by additional measurement. Three variation sources are distinguished:
between strain variability (intraspecies variability), within strain variability and analytical variability. The
between strain variability is not included in this standard as it is designed to study only one strain at a time.
The standard deviation represents the within strain biological variability associated with the parameter
3.36
water activity
a
w
ratio of the water-vapor pressure in the medium or foodstuff to the vapor pressure of pure water at the
same temperature. It represents the water available for the microorganisms to use
[SOURCE: ISO 18787:2017, 3.1, modified — The definition has been condensed and the formula and Notes 1
and 2 to entry have been removed. The sentence “It represents the water available for the microorganisms
to use” was added.]
3.37
weak acid
is characterized by its high pKa. It does not dissociate completely in aqueous solution. Acetic acid and citric
acid are examples of weak acids

oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
4 Principle
4.1 General
The general equation used to describe the effect of different independent intrinsic and extrinsic factors on
the maximum specific growth rate of a microorganism is based on a modular approach called the "gamma
[28]
concept" and described in Equation (1).
µ = μ . ɣ(T) . ɣ(pH). ɣ(a ) . ɣ (inhibitors) (1)
max w
where
-1
µ maximum specific growth rate (h ) of the studied strain in the matrix;
max
-1
μ
optimum growth rate (h ) of the studied strain in the matrix;
ɣ(T) dimensionless function describing the relative effect of the Temperature on microbial
growth;
ɣ(pH) dimensionless function describing the relative effect of the pH on microbial growth;
ɣ(a ) dimensionless function describing the relative effect of the a on microbial growth;
w w
ɣ(inhibitors) dimensionless functions describing the relative effect of different measurable inhibi-
tors like the undissociated form of the weak (organic) acids (HA) or CO .
The ɣ terms all vary between 0 and 1, ɣ = 0 when growth is fully inhibited by the studied factor, and ɣ = 1
when growth is not at all inhibited by the studied factor.
There are various secondary models available in the literature to describe the mathematical expression of
the gamma terms. In this standard, the cardinal models are used and presented in 4.2.
For the adequate use of the models and interpretation of data, knowledge of and experience in using
predictive microbiology models is essential.
4.2 Mathematical models
Under the gamma concept, the different intrinsic and extrinsic factors (e.g. temperature, pH, water activity,
inhibitors) have separate and independent effects on the maximum specific growth rate, which implies that
the cardinal values associated with a factor are also estimated separately and independently.
Various mathematical models have been developed in the literature.
— For describing the effects of temperature, one of the two following models shall be used: the CTMI
(Cardinal Temperature Model with Inflection) model (Equation 2) shall be used when optimal and super-
[25] [21]
optimal temperatures are required while the restricted Ratkowsky (linear) model (Equation 3)
shall be used when the input temperature ranges from the minimum supporting growth up to a reference
temperature that is below the optimal temperature.

oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
ɣ(T)=
0, if TT≤
 C
min


TT−TT−
()
()C
max

min
, if TT<  C
max
min
TT− TT− T−T −−TT TT+−2T
 () ()
()CC()() ()C
opt opt opttopt maxopt
min min min

 0, if TT≥
max

where
T temperature (°C);
C
T estimated minimum temperature for growth for the cardinal gamma term;
min
T estimated optimum temperature for growth;
opt
T estimated maximum temperature for growth.
max
0, if TT<

R
min


ɣ(T)= (3)

 TT− 
R
min
  , if TT>
R
min
 
TT−

R
ref
 
min
where
T temperature (°C);
R
T estimated minimum temperature for growth for the restricted Ratkowsky gamma term;
min
T refence temperature.
ref
In case the restricted Ratkowsky model is used for the gamma term to describe the effects of the temperature,
it is important not to use the model outside the experimental range on which it was developed.
[25]
— For describing the effects of pH, one of the two following models shall be used: the cardinal model in
[8]
case the regular delta shape is observed (Equation 4) or the Aryani model in case there is a plateau
observed around the optimum making it impossible to estimate pH (Equation 5).
max

0, if pH≤pH
min


pH−pH pH−pH
()
()C
max

min
ɣ(pH)= , if pH < 
minmax

pH−pH ()pH−pH −−pH ppH
()
()C
max opt
min


0, if pH≥pH
 max
where
pH hydrogen potential;
C
pH estimated minimum pH for growth for the cardinal gamma term;
min
pH estimated optimum pH for growth;
opt
pH estimated maximum pH for growth.
max
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
0, if pH ≤pH
 A
min


 pH−pH 
()
A
min

 

pH −pH
 
()
A 12/
ɣ(pH)= (5)
min

12−
 
, if pH >pH

A
  min
pH −pH
 ()ref A
min
 

 
ppH −pH
()A 12/
 

min
12−
 
where
pH hydrogen potential;
A
pH estimated minimum pH for growth for the Aryani gamma term;
min
pH at which the maximum specific growth rate μ is half of the μ .
pH
max
1/2
pH Reference pH.
ref
— For describing the effects of the aw, models based on a linear (Equation 6) or non-linear relationship such
[26]
as the cardinal aw model shown in Equation (7), shall be used:
0, if aw≤aw
 L
min


ɣ(aw)= aw−aw (6)

L
min
if aw>aw
 L
min
1−aw
L


min
where
aw water activity;
L
aw : estimated minimum water activity for growth for the linear gamma term.
min
In case a linear relationship is used to describe the effects of the a , it is important not to use the model
w
outside the experimental range on which it was developed (e.g. if experiments were performed up to 0,996 it
is not possible to extrapolate at 0,998).
ɣ(aw)=
 0, if aw≤aw
min

n

()aw−aw aw−aw
max ()C

min
, if aw < 
mminmax
n−1

aw −aw aw −awwawa− wa−−wawawa+−w na. w
() ()
()C ()()CC()
opt opt optopt maxopt
min min min


0, aw≥aw

max
(7)
where
aw water activity;
n a shape parameter
C
aw estimated minimum a for growth for the cardinal gamma term;
min w
aw estimated optimum a for growth;
opt w
aw estimated maximum a for growth.
max w
oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
NOTE most of the times n = 1 and aw is assumed to be 1,0.
max
— For describing the effects of concentrations of inhibitors including undissociated organic acids, CO2 and
others, the following equation shall be used:
α

[]Inhibitors
 
1− , if InhibitorsM< IC
 []
 
ɣ(Inhibitors)= (8)
MIC
  

0, if [Inhibitors]]≥MIC

where
[Inhibitor] concentration of the inhibitor (e.g. undissociated organic acid (mM), CO (%));
MIC Minimal Inhibitory Concentration;
α = shape parameter of the curve with:
— α = 1 the shape is linear;
— α > 1 the shape is downward;
— α < 1 the shape is upward.
NOTE when several inhibitors act in combination, several gamma terms are used.
4.3 Process of cardinal values and food correction factor determination
The cardinal values are estimated parameters associated with the chosen gamma terms. For example, the
C
cardinal values for temperature are T , T , T and allow to calculate the relative effect of temperature
min opt max
through ɣ .
(T)
The cardinal values are assumed to be specific characteristics of the studied microbial strain, and are
independent of the environment in which growth takes place. They are therefore mostly studied in broth to
simplify and automate the experiments required to determine them. The effect of the medium appears
  
through the parameter μ (see Equation 1). If the medium is a food product then μ is identified as μ
Food
 
and if the medium is broth, μis identified as μ . The food correction factor links these two parameters
Broth
(see section 4.6).
The cardinal values and the food correction factor are referred to as growth parameters. Their determination
requires three steps.
The cardinal values determination is a two-step procedure, individually applied for each studied factor.
First, the maximum specific growth rates of the microorganism are assessed in broth, for different levels
of the studied factor. Then, a secondary model (section 4.2) is used to fit the observed maximum specific
growth rates data against the different levels of the studied factor to assess the cardinal values. The third
step is the determination of the food correction factor.
Once determined and validated, the cardinal values and the food correction factor are used to predict the
behavior of the studied organism in new conditions.
4.4 Determination of the maximum specific growth rate
The maximum specific growth rates used to assess cardinal values are obtained in broth. The choice of the
appropriate broth shall be justified based on literature or on preliminary studies, as it can have an impact
[16]
on the determination of the cardinal values .

oSIST prEN ISO 23691:2024
ISO/DIS 23691:2024(en)
The maximum specific growth rate is determined for different levels of each studied factor in broth adjusted
to the test conditions (modified broth), by using one of the following methods:
(1) The binary dilution OD-based method completed by fitting a linear regression performed on the natural
logarithm of the dilution factor as function of td, the time to reach a target OD threshold.
(2) The direct plating method completed by fitting a recognized primary model to the growth kinetic data
of the studied strain in a given environmental condition.
Usually, automated Optical Density (OD) measurements with high throughput equipment are preferred to
accelerate data acquisition. In case automated equipment is not available, the maximum specific growth rate
shall be calculated through direct plating method.
When indirect methods cannot be used (e.g. for determination of maximum specific growth rates in extreme
conditions around the growth limits), direct plating shall be used.
4.4.1 Binary dilution OD-based method
-1
The maximum specific growth rate, µ (h ) is defined as follows:
max
1 dN
μ·= (9)
max
N dt
where N is the number of microorganisms at a given time, t (h).
During the exponential growth phase, µ is constant, and equation 9 can be integrated as follows:
max
N
t
ln =−μ·()t λ (10)
() max
N
where N is the number of microorganisms at t=0 and λ (h) is the lag time.
Thus, for successive binary dilution kinetics, coming from the same culture and for which the lag time could
be considered as constant, Equation (10) can be modified as indicated in Equation (11) and Equation (12).
N

d
ln =−μ · t λ
()
maxd1
()
 N

(11)

N

d
ln =−μ ·()t λ
() maxdk
N

 0k
N
ln =−μ·()tt (12)
() maxdkd1
N
0k
where
N /N the binary dilution ratio (1, 2, 4, 8…), noted D;
01 0k
t and t the detection times for dilutions 1 and k.
d1 dk
If the growth is monitored by measuring the change in Optical Density (OD) measurements over
...